Radical and its rational exponential form

In summary, the conversation discusses the equivalence of different forms of expressing (-3)^2/2, which is also equal to sqrt(9). However, in the complex numbers, it is important to choose the correct root when taking the square root.
  • #1
OceanSpring
11
0
Can someone explain how these are equivalent.

sqrt((-3)^2) = (-3)^2/2

=sqrt(9) and (-3)^1

3 is not equal to -3

(-3)^2/2 can be expressed as:

(-3^2)^1/2 and (-3^1/2)2

(9)^1/2 and (sqrt(-1)sqrt(3))^2

3 is not equal to -3

Every textbook I've come across says these forms are equivalent. This seems totally inconsistent.
 
Last edited:
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  • #2
sqrt((-3)^2) = (-3)^2/2
That is not true. This rule applies to positive numbers in the inner bracket only.

In the complex numbers, you have to choose which root you would like to take (as there are always two, apart from sqrt(0), so sqrt(9)=-3 is... well, not completely wrong, but not really right.
 

Related to Radical and its rational exponential form

What is a radical?

A radical is a mathematical symbol (√) used to indicate the root of a number. The most common radical is the square root (√), which indicates the number that, when multiplied by itself, gives the number under the radical sign.

What is the rational exponential form of a radical?

The rational exponential form of a radical is a way of writing a radical expression using exponents. It is written as a fractional exponent, where the numerator represents the power and the denominator represents the root. For example, √4 can be written as 4^(1/2).

How do you simplify a radical expression?

To simplify a radical expression, you need to find the largest perfect square that is a factor of the number under the radical sign. Then, you can rewrite the radical expression using the square root of the perfect square as the coefficient. For example, √12 can be simplified as 2√3.

What is the difference between a radical and an exponent?

A radical is a symbol used to indicate the root of a number, while an exponent is a number that indicates how many times a base number is multiplied by itself. A radical is the inverse of an exponent, and they are related through the rational exponential form.

How do you convert a radical expression into its rational exponential form?

To convert a radical expression into its rational exponential form, you need to identify the power and root of the radical. Then, you can rewrite the expression using the power as the numerator and the root as the denominator of the fractional exponent. For example, √27 can be written as 27^(1/3).

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